Modeling structural transformations in binary alloys with phase field crystals

Greenwood, Michael; Ofori-Opoku, Nana; Rottler, Jörg; Provatas, Nikolas

doi:10.1103/physrevb.84.064104

Cited by 101 publications

(115 citation statements)

References 25 publications

(42 reference statements)

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“…These goals are part of a larger effort to exploit the novel features of the PFC approach within traditional areas of materials science, including crystal plasticity, structural phase transformations, and microstructure evolution [21][22][23][24][25][26]. Some initial groundwork covering fundamental dislocation properties in FCC materials was reported by the present authors in Ref.…”

Section: Introductionmentioning

confidence: 92%

Phase field crystal modeling as a unified atomistic approach to defect dynamics

et al. 2014

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Material properties controlled by evolving defect structures, such as mechanical response, often involve processes spanning many length and time scales which cannot be modeled using a single approach. We present a variety of new results that demonstrate the ability of phase field crystal (PFC) models to describe complex defect evolution phenomena on atomistic length scales and over long, diffusive time scales. Primary emphasis is given to the unification of conservative and nonconservative dislocation creation mechanisms in three-dimensional FCC and BCC materials. These include Frank-Read-type glide mechanisms involving closed dislocation loops or grain boundaries as well as Bardeen-Herring-type climb mechanisms involving precipitates, inclusions, and/or voids. Both source classes are naturally and simultaneously captured at the atomistic level by PFC descriptions, with arbitrarily complex defect configurations, types, and environments. An unexpected dipole-to-quadrupole source transformation is identified, as well as various new and complex geometrical features of loop nucleation via climb from spherical particles. Results for the strain required to nucleate a dislocation loop from such a particle are in agreement with analytic continuum theories. Other basic features of FCC and BCC dislocation structure and dynamics are also outlined, and initial results for dislocation-stacking fault tetrahedron interactions are presented. These findings together highlight various capabilities of the PFC approach as a coarse-grained atomistic tool for the study of three-dimensional crystal plasticity.

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Section: Introductionmentioning

confidence: 92%

Phase field crystal modeling as a unified atomistic approach to defect dynamics

et al. 2014

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“…The effect of large wavenumber correlations on defect stability can be demonstrated through an examination of the PFC model formulation of Greenwood et al [25][26][27] (XPFC). This approach allows one to stabilize many different crystal symmetries by constructing a correlation kernel with peaks, typically Gaussians, located at the first few primary reflections of a given lattice structure.…”

Section: Many-peaked Xpfc Modelmentioning

confidence: 99%

Defect stability in phase-field crystal models: Stacking faults and partial dislocations

et al. 2012

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The primary factors controlling defect stability in phase-field crystal (PFC) models are examined, with illustrative examples involving several existing variations of the model. Guidelines are presented for constructing models with stable defect structures that maintain high numerical efficiency. The general framework combines both long-range elastic fields and basic features of atomic-level core structures, with defect dynamics operable over diffusive time scales. Fundamental elements of the resulting defect physics are characterized for the case of fcc crystals. Stacking faults and split Shockley partial dislocations are stabilized for the first time within the PFC formalism, and various properties of associated defect structures are characterized. These include the dissociation width of perfect edge and screw dislocations, the effect of applied stresses on dissociation, Peierls strains for glide, and dynamic contraction of gliding pairs of partials. Our results in general are shown to compare favorably with continuum elastic theories and experimental findings.

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“…To construct a phase diagram, a density mode approximation is introduced for each of the crystal structures of interest, inserted into the free energy and after following standard minimization techniques (see Appendix of Ref. [20]), the phase diagram shown in Fig. 1 is attained.…”

Section: Equilibrium Propertiesmentioning

confidence: 99%

“…Greenwood et al [18,19] accomplished this by introducing a class of multi-peaked, two-point direct correlation functions in the free energy functional that contained some of the salient features of CDFT, yet were simplified to be numerically efficient. This XPFC formalism was later extended to binary [20] and N -component [21] alloying systems, and applied to phenomena such as dendritic and eutectic solidification [21], elastic anisotropy [20], solute drag [22], quasi-crystal formation [23], solute clustering and precipitation mechanisms in Al-Cu [24] and Al-Cu-Mg [21,25] alloys, and 3D stacking fault structures in fcc crystals [26].…”

Section: Introductionmentioning

confidence: 99%

Complex order parameter phase-field models derived from structural phase-field-crystal models

et al. 2013

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The phase-field-crystal (PFC) modeling paradigm is rapidly emerging as the model of choice when investigating materials phenomena with atomistic scale effects over diffusive time scales. Recent variants of the PFC model, so-called structural PFC (XPFC) models introduced by Greenwood et al., have further increased the capability of the method by allowing for easy access to various structural transformations in pure materials [Phys. Rev. Lett. 105, 045702 (2010)] and binary alloys [Phys. Rev. B. 84, 064104, (2011)]. We present an amplitude expansion of these XPFC models, leading to a mesoscale complex order-parameter (amplitude), i.e., phase-field representation, model for two dimensional square-triangular structures. Amplitude models retain the salient atomic scale features of the underlying PFC models, while resolving microstructures on mesoscales as in traditional phase-field models. The applicability and capability of this complex amplitude model is demonstrated with simulations of peritectic solidification and grain growth exhibiting the emergence of secondary phase structures.

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Modeling structural transformations in binary alloys with phase field crystals

Cited by 101 publications

References 25 publications

Phase field crystal modeling as a unified atomistic approach to defect dynamics

Phase field crystal modeling as a unified atomistic approach to defect dynamics

Defect stability in phase-field crystal models: Stacking faults and partial dislocations

Complex order parameter phase-field models derived from structural phase-field-crystal models

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